Skip to main content

Gentzen-type systems and resolution rules part I propositional logic

  • Conference paper
  • First Online:
COLOG-88 (COLOG 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 417))

Included in the following conference series:

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abdali M.,Manna Z.: Nonclausal temporal deduction, Lecture Notes in Computer Sci. 193, Springer-Verlag, Berlin, Heidelberg, New York (1985), 1–15

    Google Scholar 

  2. Auffray Y.: Linear strategy for propositional modal resolution. Inform. Process. Lett. 28, (1988), N2, 87–92

    Google Scholar 

  3. Bazylev Ju.: Resolution theorem prover for S4. (Russian). To appear in Proc. Soviet Academy of Sci., Techn. Cybernet.

    Google Scholar 

  4. Cavalli R., Fariñas C.L.: A decision method for linear temporal logic. Lecture Notes in Computer Sci. 170, (1984), 113–127

    Google Scholar 

  5. Chan M.C.: The recursive resolution method for modal logic. New Gener. Comput. 5, (1987), N2, 155–184

    Google Scholar 

  6. Chang C., Lee R.: Symbolic Logic and Mechanical Theorem Proving. Academic Press, New York, 1973

    Google Scholar 

  7. Ceitin G.S.: On the complexity of proofs in propositional calculus. English translation: Seminars in Math.. Plenum Publishers, 8, (1970)

    Google Scholar 

  8. Cialdea M.: Some remarks on the possibility of extending resolution proof procedures to intuitionistic logic. Inform. Process. Lett. 22, (1986), N2, 87–90

    Google Scholar 

  9. Cialdea M., Fariñas del Cerro C.L.: A modal Herbrand's property. Z. Math. Logik Grundlag. Math. 32, (1986), N6, 523–530

    Google Scholar 

  10. Curry H.: Foundations of Mathematical Logic, McGraw-Hill, New York, 1963

    Google Scholar 

  11. Fariñas del Cerro C.L.: Un principle de résolution en logique modale. RAIRO Inform. Theor. 18, (1984), N2, 161–170

    Google Scholar 

  12. Fariñas del Cerro C.L.: Resolution modal logic. Automated Reasoning in non-classical logic. Logique et Anal. 110/111, (1985)

    Google Scholar 

  13. Fariñas del Cerro C.L.: MOLOG: A system that extends PROLOG with modal logic. New Gener. Comput., 4, (1986), 35–51

    Google Scholar 

  14. Farinas del Cerro C.L., Herzig A.: Linear Modal Deductions. Lecture Notes in Computer Sci., 310. Springer-Verlag, Berlin, Heidelberg, New York (1989), 487–489

    Google Scholar 

  15. Fitting M.: First order modal tableaux. J. Autom. Reasoning, (1988), N4, 191–213

    Google Scholar 

  16. Fitting M.: Resolution for intuitionistic logic. Methodologies for Intelligent Systems. pp 400–407, North-Holland, Amsterdam, 1987

    Google Scholar 

  17. Kleene S.: Introduction to Metamathematics. North-Holland, Amsterdam, 1952

    Google Scholar 

  18. Kleene S.C.: Permutability of inferences in Gentzen's calculi LK and LJ. Memoirs of the American Math. Soc. 10, (1952)

    Google Scholar 

  19. Lifschitz W.: What is the inverse method? J. Autom. Reasoning, (1989)

    Google Scholar 

  20. Manna Z., Waldinger R.: A deductive approach to program synthesis. J. Assoc. Comp. Mach. Trans. Prog. Lang. Syst. 2, (1980), N1, 90–121

    Google Scholar 

  21. Manna Z., Waldinger R.: Special relations in automated deduction. J. Assoc. Comp. Mach., 33, (1986), N1. 1–59

    Google Scholar 

  22. Manna Z., Waldinger R.: Deductive synthesis of the unification algorithm. Sci. Comput. Programming, 1, (1981), 5–48

    Google Scholar 

  23. Maslov S.: Inverse method of establishing deducibility. (Russian). Trudy Mat. Inst. Steklov. 98, (1968), 26–87. (Translated by Amer. Math. Sci.)

    Google Scholar 

  24. Maslov S. Ju.: Proof search strategies based on the ordering in a favorable set. Seminars in Math., Plenum Publishers, 16, (1971)

    Google Scholar 

  25. Maslov, S. Ju.: Connection between the strategies of the inverse method and the resolution method. Seminars in Math., Plenum Publishers, 16. (1971)

    Google Scholar 

  26. Maslov S.: Theory of deductive systems and its applications. MIT Press, Cambridge, 1987

    Google Scholar 

  27. Mints G.: Resolution calculi for the non-classical logics. (Russian). 9 Soviet Symp. in Cybernetics. Moscow, VINITI, 1981

    Google Scholar 

  28. Mints G.: Resolution calculi for the non-classical logics. (Russian). Semiotics and informatics, 25, (1985), 120–135

    Google Scholar 

  29. Mints G.: Resolution calculi for modal logics. (Russian). Proc. Estonian Acad. of Sci. (1986), N3, 279–290

    Google Scholar 

  30. Mints G.: Cutfree formalisations and resolution methods for propositional modal logic. VIII Intern. Congress for Logic, Methodology and Philosophy of Science, Moscow 1987, 46–48

    Google Scholar 

  31. Murray N.V.: Completely nonclausal theorem proving. Artificial Intelligence 18, (1982), N1, 67–85

    Google Scholar 

  32. Murray N., Rosenthal E.: Inference with path resolution and semantic graphs. J. Assoc. Comp. Mach. 34, (1977), N2, 225–254.

    Google Scholar 

  33. Nepeivoda N.N.: Prefix semantic tables for modal logics (Russian). Many-valued, relevant and paraconsistent logics. Moscow, 1984, 78–91

    Google Scholar 

  34. Ohlbach H.: A resolution calculus for modal logics. Lecture Notes in Computer Sci., 310, Springer-Verlag,Berlin, Heidelberg, New York (1988), 500–516

    Google Scholar 

  35. Shvarts G.: Gentzen Style Systems for K45 and K45D. Lecture Notes in Computer Sci. 363, Springer-Verlag,Berlin, Heidelberg, New York (1989) 245–256

    Google Scholar 

  36. Traugott: Nested Resolution. Lecture Notes in Computer Sci., 230, Springer-Verlag, Berlin, Heidelberg, New York (1986)

    Google Scholar 

  37. Venkatesh G.: A decision method for temporal logic based on resolution. Lecture Notes in Computer Sci. 206, Springer-Verlag, Berlin, Heidelberg, New York (1985), 273–288

    Google Scholar 

  38. Volozh B.,Matskin M.,Mints G., Tyugu E.: The PRIZ system and propositional calculus. Cybernetics 18, (1982), N6, 777–788

    Google Scholar 

  39. Vorobyev N.N.: A new derivability algorithm in the constructive propositional calculus. Trudy Math. Inst., Steklov. 52, (1958), 193–226. (Russian, the English translation by Appl. Math. Sci.)

    Google Scholar 

  40. Wajsberg M.: Untersuchungen ueber den Aussagenkalkuel von A. Heyting, Wiadomosci Matematyczne, 46, (1938), 45–101

    Google Scholar 

  41. Zamov N.: Maslov's inverse method and decidable classes. Ann. Pure and Appl. Log., 42, (1989), 165–194

    Google Scholar 

  42. Zamov N.: Resolution without Skolemization. Doklady Akad. Nauk SSSR, 293, (1987), N5, 1046–1049

    Google Scholar 

  43. Zamov N.: A resolution system for S4. To be submitted

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Per Martin-Löf Grigori Mints

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mints, G. (1990). Gentzen-type systems and resolution rules part I propositional logic. In: Martin-Löf, P., Mints, G. (eds) COLOG-88. COLOG 1988. Lecture Notes in Computer Science, vol 417. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52335-9_55

Download citation

  • DOI: https://doi.org/10.1007/3-540-52335-9_55

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52335-2

  • Online ISBN: 978-3-540-46963-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics